X3735

X75com(1st BROCARD TRIANGLE)

X3735 = X75-of-1st-Brocard-triangle
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 32 }: Central Line L(1, 32) { 76, 257 }: Central Line L(76, 257) { 37, 517 }: Central Line L(37, 517) { 6, 758 }: Central Line L(6, 758) { 75, 712 }: Central Line L(75, 712) { 39, 986 }: Central Line L(39, 986) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_712 = EVEN (- 3, - 2) INFINITY POINT (0.0337, -0.1011) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_3735 = com(1st BROCARD TRIANGLE) (0.5463, 0.1966) A B C X1 X32 X76 X257 X37 X517 X6 X758 X75 X712 X39 X986 X3735 (a, b, c) = (5, 6, 7) | AB = 1

X3735 (X75com(1st BROCARD TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{3} + c^{3} + abc)\)
Search Value (6, 9, 13): \(2.411159317335\)
▸ Incident Central Lines16 lines

{1, 32}, {2, 3125}, {6, 758}, {37, 517}, {38, 2170}, {39, 986}, {75, 712}, {76, 257}, {392, 3290}, {762, 3617}, {766, 3056}, {980, 1959}, {982, 1015}, {984, 1573}, {2549, 2795}, {2809, 3242}

▸ Functional Relations4 relations